A gay man in an inheritance dispute asks a court to declare him the common-law husband of his late companion

WASHINGTON—A gay man locked in an inheritance dispute is asking a District of Columbia court to declare him the common-law husband of his late companion, opening a new front in the struggle over same-sex marriage.

The district has been issuing marriage licenses to same-sex couples since March 2010, but Michael Kelly and James Spellman never obtained one. Mr. Spellman says the pair lived together from 1995 until Mr. Kelly died in...